A062394 a(n) = 6^n + 1.

2, 7, 37, 217, 1297, 7777, 46657, 279937, 1679617, 10077697, 60466177, 362797057, 2176782337, 13060694017, 78364164097, 470184984577, 2821109907457, 16926659444737, 101559956668417, 609359740010497, 3656158440062977

Offset: 0

Author

Henry Bottomley, Jun 22 2001

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..150
• Amelia Carolina Sparavigna, Some Groupoids and their Representations by Means of Integer Sequences, International Journal of Sciences (2019) Vol. 8, No. 10.
• Index entries for linear recurrences with constant coefficients, signature (7,-6).

Crossrefs

Sequences of the form m^n + 1: A000012 (m=0), A007395 (m=1), A000051 (m=2), A034472 (m=3), A052539 (m=4), A034474 (m=5), this sequence (m=6), A034491 (m=7), A062395 (m=8), A062396 (m=9), A062397 (m=10), A034524 (m=11), A178248 (m=12), A141012 (m=13), A228081 (m=64).

Cf. A000400.

Programs

Magma

[6^n + 1: n in [0..30] ]; // Vincenzo Librandi, Apr 30 2011

Mathematica

6^Range[0,30] +1
LinearRecurrence[{7,-6},{2,7},30] (* Harvey P. Dale, Aug 11 2015 *)

PARI

vector(20, n, n--; 6^n + 1) \\ Michel Marcus, Jun 11 2015

SageMath

[6^n+1 for n in range(31)] # G. C. Greubel, Mar 11 2023

Formula

a(n) = 6*a(n-1) - 5.

a(n) = A000400(n) + 1.

a(n) = 7*a(n-1) - 6*a(n-2).

From Mohammad K. Azarian, Jan 02 2009: (Start)

G.f.: 1/(1-x) + 1/(1-6*x).

E.g.f.: exp(x) + exp(6*x). (End)